Nonlinear and Non-Stationary Time Series Modeling and Its Applications

University Of North Carolina At Charlotte, Charlotte NC

Investigators

Abstract

This proposal concerns scientific research and education on a variety of statistical methodological developments and foundational research with particular applications in economics and other applied fields and it consists of two subjects. The first subject is to study a new class of nonlinear seasonal time series models to characterize the seasonal variations in nonlinear and non-stationary time series. The models are decomposed into a common trend function over periods and additive seasonal effect functions that are specific to each season within the periods. Also, the models will be extended to the time-varying coefficient seasonal time series models to include exogenous variables. The nonparametric techniques will be developed to estimate the trend and seasonal effect functions and the asymptotic properties of all the proposed estimators will be established under the strong mixing conditions without any specification of the error distribution. The second subject is to develop the nonparametric modeling methods to analyze nonlinear and non-stationary time series data by considering the following nonparametric or semi-parametric models: the time-varying coefficient time series regression models with nonlinear time trend function and/or integrated regressors and/or correlated errors, the nonparametric or semi-parametric co-integration models, and the nonparametric or semi-parametric (dynamic) panel models with nonlinear time trend function and/or integrated regressors and/or correlated errors. The central components of this proposal are the developments of nonparametric modeling techniques to those models and to make those models practically useful. Specifically, the local linear model-fitting scheme will be developed to estimate the nonparametric time trend and the coefficient functions and the nonparametric regression functions. Moreover, the asymptotic properties of all the proposed estimators will be established under some regularity conditions without specifying the error distribution. Particularly, the attention will be paid on the asymptotic properties for the non-stationary cases due to different rates of convergence (by comparing with the stationary cases). Further, the bandwidth selection issue will be addressed particularly for the non-stationary cases. Finally, to test the misspecification and stationarity, a nonparametric version of the generalized likelihood ratio test together with a simple nonparametric version of bootstrap will be proposed and investigated. The intellectual merit of this proposal is not only to propose and develop several nonlinear and non-stationary time series regression models but also develop novel nonparametric modeling methodologies to make these models practically applicable. The new statistical methods will possess the advantage of requiring fewer assumptions than previously developed methods. Hence, the conclusions obtained from them should be less dubious. The broader impacts of this proposal are that this proposal represents a comprehensive and long-term attack on a host of important data analytic problems in applied fields and that the results will be of long-term theoretical and practical interests and will provide near-term solutions to real-world problems. The methods are based on the transparent ideas that can be easily incorporated into the classroom and graduate students are presently involved in the various projects described and more will become involved.